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# Uniform Acceleration

## Define and calculate uniform acceleration using formulas

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Practice Uniform Acceleration

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Uniform Acceleration

Credit: Justin De La Ornellas
Source: http://www.flickr.com/photos/ornellas/8869268939/

After jumping, this cliff diver undergoes effective free fall. Cliff diving is a sport in which athletes twist and flip on their way down. Even with the air resistance, these divers will accelerate the whole way down.

### Uniform Acceleration

Acceleration that does not change in time is called uniform or constant acceleration.  The velocity at the beginning of the time interval is called initial velocity, vi\begin{align*}v_i\end{align*}, and the velocity at the end of the time interval is called final velocity, vf\begin{align*}v_f\end{align*}.  In a velocity versus time graph for uniform acceleration, the slope of the line is the acceleration. The equation that describes the curve is vf=vi+at\begin{align*}v_f = v_i + at\end{align*}.

Example 1

If an automobile with a velocity of 4.0 m/s accelerates at a rate of 4.0 m/s2 for 2.5 s, what is the final velocity?

vf=vi+at=4.0 m/s+(4.0 m/s2)(2.5 s)=4.0 m/s+10. m/s=14 m/s\begin{align*}v_f = v_i + at = 4.0 \ \text{m/s} + (4.0 \ \text{m/s}^2)(2.5 \ \text{s}) = 4.0 \ \text{m/s} + 10. \ \text{m/s} = 14 \ \text{m/s}\end{align*}

Example 2

If a cart slows from 22.0 m/s with an acceleration of -2.0 m/s2, how long does it require to get to 4 m/s?

t=vfvia=18 m/s2.0 m/s2=9.0 s\begin{align*}t=\frac{v_f-v_i}{a}=\frac{-18 \ \text{m/s}}{-2.0 \ \text{m/s}^2}=9.0 \ \text{s}\end{align*}

### Summary

• Acceleration that does not change in time is uniform, or constant, acceleration.
• The equation relating initial velocity, final velocity, time, and acceleration is vf=vi+at\begin{align*}v_f = v_i + at\end{align*}.

### Review

1. If an object has zero acceleration, does that mean it has zero velocity?  Give an example.
2. If an object has zero velocity, does that mean it has zero acceleration?  Give an example.
3. If the acceleration of a motorboat is 4.0 m/s2, and the motorboat starts from rest, what is its velocity after 6.0 s?
4. The friction of the water on a boat produces an acceleration of -10. m/s2. If the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s?

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